三个位置有0个偶数，即全为奇数，共有5×5×5=125（种)不同元素；三个位置有2个是偶数，另一个为奇数，共有C5×4×4=240（种)不同元素，125+240_365所以入为偶数的概率为-729729（3）首先将N中任意元素各位置上的数字，若为奇数记成0,若为偶数记成1.从元素改写后的 N中任取两个元素入和μ,因为入αμ=O,所以入和μ相同位置不能同为1.所以下列(n十1)个元素可以在同一个集合中:① 000...0;2 100...0,010...0,...,00..·10,00...01.下证，元素改写后的N中的元素个数不超过n十1.假设N中含有m（m≥n十2)个元素，排成如下m行n列：a11a12.…alna21a22d2r其中aj∈{0,1},i=1,2,...,m,j=l,2,..·,n,amlam2记第i行的和S：=ai，第j列的和T;ai,则S1+S2+·.·+Sm=T+T2+...+Tn.i=1‘+u

万唯中考《定心卷》考前7天最后一卷6.电影《哪吒之魔童闹海》深受人们的喜爱.老师为激励在学中表现优异的同学，购买了2张哪吒卡片和2张敖丙卡片（除正面图案外，背面完全相同）作为奖品，将这4张卡片洗匀背面朝上置于桌面上，小明随机抽取2张，则抽取的2张卡片均是哪吒的概率为1A.6B.11C.7.嘉嘉在求解关于x的一元二次方程2x²-kx-1=0时，抄错了k值的正负号，解出x的一个根为-2，则下列结论说法正确的是结论一：原方程有两个不相等的实数根；1A.结论一正确、结论二不正确B.结论一不正确、结论二正确C.结论一正确、结论二正确D.结论一不正确、结论二不正确8.如图3,在面直角坐标系中,已知点A(0,4),B(3,0),C(0,3),若在线段AB上存在一点D,使得△ACD与△AOB是位似图形，则点D的横坐标为129B.C.D.425425C图3图4图59.如图4,AD=BC,AD/BC,AC交BD于点P,E,F分别是AD,DC的中点,选择图中的四个点为顶点画四边形，其中能画出的行四边形有A.2个B.3个C.4个D.5个10.嘉嘉和淇淇对5个正整数进行规律探究，嘉嘉写出三个连续偶数：α,a2,a（a

如图，PA是圆柱的母线，AB是底面圆的直径，C是底面圆周上异于A，B的出#客0共，小#共#大本#若#，三欧日.物楼ATY（2）若M是PC的中点，求三棱锥BACM的体积一点，且PA=AC=BC=2.（1）求证：BC⊥面PAC；24.（本小题满分10分）25.（本小题满分10分）（2）求 sin A 的值（1）求b；

C.40~80℃时，温度每数学卷D要使硫酸钠的溶解度6.如图，边长为4的正方开的边相切），设点B到说明：1.全卷满分120分，考试时间120分钟。2.请将答案写在答题卡上，否则不给分。A.3种二、填空题（本大题共67.若一个角的余角为368.为进一步提高生态功省财政厅下达2025全七位，还得到了π的两个近似值：22长10%.数据5.5亿9.在面直角坐标系中22约率10.按一定规律排列的题11.如图，在矩形ABCDB.负分数A.整数C.无理数D正分数于点E，则cosLD2.数学中的对称美，令人赏心悦目，英文字母中同样有对称美，对称的英文为symmetry，下列选项分别是s,y,m,e艺术字的图案，其中属于中心对称图形的是mmJV不12.如图，△ABC是等BE.若△CDF中A内3.下列运算中，正确的是（-a²)=aD.(a+b)²=a²+b²A3a+4a=7a²线4.某班数学兴趣小组调查了全班50名学生每周做家务的时间，根据调查所得的数据制成如图所示的条三、解答题（本大题该班学生每周做家务时间的均数（单位：小时）为封M10人数/人13.（1）计算：2025930F（2）化简：m-密26252015101.52 时间/小时0.514.今年植树节D.13C.1(1）“该班的B.0.98A.0.88（2）若该班↑y/g48.843.719.52040【数学（第1页）】

下面证明：a≥时，h(x)≤0恒成立:h（x)=Inx-a（x)≤Inx.12分x2x-1-x-(x-1)²令p(x)=Inx--(x--),x≥1;p'(x)=:0>2x22x2Y(x)在[1,+∞o)单调递减;又x≥1,.p(x)≤p(1)=0 ;g(x)≤(x)≤0恒成立，证毕..15分18．（1）由题意可得，椭圆E左右顶点A,A分别为(-√3,0)(√3,0)，而双曲线的顶点与A,A重合.故可设x²y²双曲线的标准方程为-=1(a,b>0)，此时a=√3;_2由e==2√3-得c=2,b²=c²-a²=4-3=13x²因此双曲线的标准方程为=1.3分3（2）（i）由题意可得，切线I的斜率存在，不妨设l:y=kx+m，切点R(xo,y。),联立方程：[x²-3y²=3整理可得：（1-3k²)x²-6mkx-3m²-3=0，由于1与双曲线相切：因此△=0，即[y= kx+m36m²k²+12(m²+1(1-3k²)=0，经化简可得：m²+1=3k²（*)...5分3mkm此时x=mx=0，.7分k若点 R,M,N 的横坐标成等差数列,3mk2m√3则2xM=x+x，即若m=0，则根据（*）式可得，k=±此时1为双曲线1-3k2k33k2√6的渐近线，不可能为切线，故解得3k²=2，:.k=（切点在第一象限）..9分k3（ii）不妨设P(x,y),Q(x2,y2)，此时切线l:y=kx+m与椭圆联立:x²+3y²=3，整理得：（1+3k²)x²+6mkx+3m²-3=0（※）[y = kx + m（※）式中，△=36k²-12m²+12=24>0恒成立.11分m√6 |m|此时 Sopp =|PQl·do-pQ =3.14分1+3k²√1+k²1+3k21+3k24

四、解答题：本题共5小题，共77分.解答应写出文字说明、证明过程或演算步骤15.（13分）),n=(sin x,cos x),x∈ (o,)-（1）若m⊥n，求tanx的值；（2）若m与n的夹角为，求x的值16.（15分）已知向量a=（cosx，sinx），b=（3，一√3），x∈0，π]（1）若a//b，求x的值；（2）记f（x）=a·b，求f（x）的最大值和最小值以及对应的x的值【2026高考真题分类卷·数学（十）第3页（共6页）】

41-45 CBADC46-50 BCADB51-55 DBACA56. impressive57.and58.learning59. which60. dies61. where62. found63. In64. previously65.belocated写作第一节【写作提示】本写作要求写一篇有关学校正能量墙的报道。第一段应介绍此次活动的目的（如鼓励学生分享令人振奋的故事和照片，营造充满正能量的校园环境等）；第二段应介绍活动过程（如同学们热情地聚集在一起，对墙进行个性化改造等）；第三段可写同学们对这次活动的反响（如同学们对有机会分享表示感谢，这面墙提醒每个人积极性在我们生活中的变革力量等）。One possible version:Last Saturday, our school launched a “Positive Energy Wall' to inspire students and promotepositivity. This initiative aimed to encourage students to share uplifting stories and photos,promotinga supportivecommunity.During the event, students enthusiastically gathered to personalize the wall, displaying theirexperiences and images that contain hope and courage. Many shared stories of overcomingchallenges and acts of kindness. The wall quickly became a special place.The response was positive with students expressing gratitude for the opportunity to share.Thewall has become a powerful symbol of encouragement, leaving positive comments and happysmiles. It will remind everyone of the power of positivity in our lives.第二节【写作提示】材料讲述了MrLim失业三个月且求职无果，妻子为维持生计去海外工作，他独自照顾两个孩子。Luke和Lisa为让父亲开心，在其生日当天买蛋糕、在墙上作画准备惊喜。父亲回家后却因墙被乱画斥责孩子们，蛋糕也被不小心损坏。最终，Lisa哭着说出他们在墙上作画是为给父亲生日惊喜。第一段给出句描述了MrLim走向Luke，续写时可以围绕MrLim意识到自己的错误而道歉展开。比如，他道歉的话语，孩子们对父亲道的反应，宜展现矛盾化解后的温馨。第二段给出句描写了孩子们唱生日歌，本段可进一步描写生日聚会后续的温馨场景。可以通过一些细节描写，如孩子们满足的笑容、MrLim眼中的欣慰等，来突出这个特别的生日给家庭带来的积极变化，让家庭情感的升温更加具体可感。Onepossibleversion:Hearing that, Mr Lim fell silent for a moment before approaching Luke. Sensing a presencenearing, Luke tensed up. He did not want the worst to happen. Instead of giving a physicalpunishment, Mr Lim wiped away the boy's tears. Gently,Mr Lim whispered,I' m so sorry, Son. Ihad a really rough day trying to find a job, but I shouldn't have taken my anger out on you guys."Then, Mr Lim held his children in a warm embrace.After the tension eased,Luke and Lisa sang a birthday song for Mr Lim. Even though the birthdaycake had been ruined, Mr Lim still thanked his children for the surprise and planted a kiss on eachof their cheeks. He added that the painting on the wall was beautiful and it should be left thereindefinitely. Luke and Lisa glanced at each other. They smiled. That night, as they ate the ruined

重拾对人性的信任。失而复得的钻石是一份礼物，更是人性善意的见证。【知识链接】sicktosb'sstomach：非常担心C篇主题语境：人与自然一一环境保护本文是说明文。美国加州普莱瑟县通过购买264英亩MourierWest土地，保护濒危物种栖息地。28.C。推断。根据第一段中的amajorlandbuyaimedatprotectingimportanthabitatforendangeredanimals（一项旨在保护渺危动物重要栖息地的大型土地收购）和第二段中的Thedeal...ispartofa largerefforttobalancerapidgrowthwithenvironmental protection（这笔交易是衡快速发展与环境保护的重要举措）可知，这笔土地交易的核心是保护自然栖息地。29.C。推断。根据第三段可知，MourierWest区域里的i旧稻田防洪堤形成了许多季节性湿地，这些湿地成为独特野生动物的安全港湾。其中最引人注目的是联邦级危物种-vernalpoolfairyshrimp（春池神仙虾）。此外，Pleasant GroveCreek也流经这片土地，MourierWest也为十多种其他受保护动物提供了生存所需的环境与资源。这些信息都表明MourierWest在维系当地生物多样性、支撑生态衡中的关键作用。B项（有大片稻田）错误，根据本段中的oldricefieldlevees（旧稻田防洪堤）可知，稻田已不存在。30.D。理解词汇。根据第二段中的Thedeal，fundedbytheCaliforniaDepartmentofFishandWildlife和划线词后的It'sagreatpictureofhowdifferentlevelsofsupportcanworktogetherforsomethingatthelocallevel（这充分体现了不同层级的支持力量如何协同合作，为地方事务出力）可知，地方资金和联邦政府的资金在保护那些原本可能因开发而消失的土地方面发挥了很大的作用，leverage强调通过利用政府资金来达成某个目标，在本段中表示“借助，利用”。31.A.理解具体信息。根据最后一段中的thePlacerCountyConservationProgramhasprotectedabout 4,8o0 acres...thelong-termgoal isnearly ten times that amount,protecting tensofthousandsofacres可知，PlacerCountyConservationProgram已保护约4，8oo英亩土地，其长期目标是这一数字的近十倍，要保护数万英亩土地，所以，该项目的下一步是保护更多土地。B项（设定长期目标）错误，文中提到长期目标已存在：C项（减少开发）错误，文中未提及：D项（启动更多类似项目）错误，文中强调的是扩大保护面积而非启动新项目。D篇主题语境：人与社会一一科学与技术本文是说明文。英伟达公司推出了人工智能手语学台Signs，该台能辅助用户学美国手语，未来还将完善更多功能。32.D。理解具体信息。根据第一段的内容和第二段中的NVIDIAintroduceda languagelearningplatformusingartificial intelligence(Al)thatpromisestodojustthatforAmericanSignLanguage（ASL）learners可知，英伟达公司推出了一个利用人工智能的语言学台Signs，该台帮助用户学美国手语。33.B。理解具体信息。根据第五段中的MichaelBoone，themanagerfortrustworthyAlproductatNViDlA,said the company isfocused on creating Al toolsnotjust forbusinesses,butalso tosupportreal-lifeusesforthetechnology可知，英伟达公司的MichaelBoone表示，公司开发Signs这类人工智能工具的目的不仅是为了企业，更是要支持该技术在现实生活中的应用。34.B。理解篇章结构。第六段中的Signsisfreetouse，anditwillallowASLspeakerstocontributevideosofsignsthatarenotalreadyavailableontheplatform表明，用户可以上传台上尚未有的手语视频。随后作者指出，这些数据（Thatdata）能帮助英伟达公司开发新产品。因此，

学科网组卷网VII1.阅读理解（共20小题；每小题2分，满分40分）第一节阅读下列短文，从每小题所给的A、B、C、D四个选项中选出一个最佳选项。AWant to enjoy exercise at home?Click here and you can get some online sports classesforfree!LIUGENGHONG'SSHUTTLECOCKEXERCISEBuild strong bodies in a fantasticway!you tokeep going until the last minute and you can burn your fat fast.Time: 7 p m.-8:30 p.m. on weekdays9a.m.-10:30a.m.atweekendsLATINDANCEWITHKARENEnjoy yourself and get fit!Doyoulove dancingandparties?Well,Latin dance isforyou.You can dance togreatmusicandbun1,oo0calories（卡路里）anhour.Karenis anexperiencedLatin dancetrainerandmanypeoplelikeherclassesverymuch.Time: 2 p.m.-4 p.m. on weekdays9 a.m.-11 a.m.at weekendsYOGA WITH SARAExerciseyourbody!Sara'syoga classes are for people who want to improve their strength and shape theirbodies. Sara has trained in different styles of yoga.4p.m.-5p.m.everyTuesdayandThursdayforexperiencedlearnersJOHN'SSPINCLASSESHave a good time on a bike!Spinclassesareasafe andgreatwaytoworkout—it doesn’tmatterhowoldyou areorhow fit you are.John is a wonderful spin trainer.He will encourage you to do your best in everyclass.第7页/共19页

2024-2025学年度下学期双语学报第T6期Student九年级TimesX版践行课程标准发展核心素养杭州专版扫码获取配报资源双语学报社编辑出版 总主编 刘兆义国内统一连续出版物号CN34-0030总第5233期2025年6月26日第T1期W:No.My parents won't be in New York around74.will stop75.whatB1版Keys:A 1-5 CADCA B1-5BDADAChristimas. They're traveling around the第四部分：B2B3B4版Keys:world now.Now they're touring around Italy【写作指导】中考英语全真模拟训练（一）and around Christmas I guess they'll be in1.任务分析听力原文及参考答案Southern China.本篇书面表达要求写一封邮件介绍一种时听力原文M:So will you stay in Chicago for Christmas?间管理方法。第一节：W:No.I'm thinking about going to New Zealand主题：人与自我之生活与学听下面5段对话。每段对话后有一个小for two weeks. I've been there once. But I文体：应用文题，从题中所给的A、B、C三个选项中选出最didn't have time to see much of it because I时态：以一般现在时为主佳选项，并标在试卷的相应位置。听完每段对only spent three days therebecause ofmywork.人称：以第一人称为主话后，你都有10秒钟的时间来回答有关小题M:The country is really worth a visit.Have you2.行文布局和阅读下一小题。每段对话仅读一遍。booked the air ticket yet?本篇书面表达可按照以下框架完成。1.M:Iwant to takeatiptoeijing and ShanghaiW: Not yet. I'm planning to book it a few days开头：简单问候，引出写作话题before Christmas.主体：描述一种时间管理方法、优点和感受one day How about you,Ann?M:Wellthelonger youwaitthemore epenivW:WellIused to consider visiting London or结尾：表达希望或祝福3.可用句型itwillbe.In fact,the prices may double atNew York.But now I plan to go to Shenzhen.Christmas time. So why not book it now?引出话题：2.W:I don’t likevegetables.Ionly eat them forW:Then I'll do it this afternoon.What is yourNow let me share one of my ways with you.dinner.plan for Christmas? Will you travel to anyI want to tell you how I manage my time.M:Well, I'm different. I usually have themplace?You've had a very long year.YouTime ismportant forus studentsandIhavefor breakfast lunch and supper.should have a relaxing holiday.found a good way to use it well.3.M:JaneI hear your English is excellent.Righ介绍方法与优点：W:Maybe,Paul.However,my friend Lisa isI make a to-do list every morning and follow itbetter at the subject than me.think I should go?听下面一段独白，回答第11至第15五个during the day.M: But both of you are better at English thanIalways do my homework from 6:30 to 8:00 in小题。me!W) Hi,Mike, this is Lydia. I need yourhp.the evening.4.M:Oh,no!It’s already ten to seven.Come on,I'm flying back to New York tomorrow morning.I follow the list and finish the tasks one by one.or we'll miss the start of the movie.This helps me stay focused and do things stepW:No hurry. The movie will begin in half anMy plane is leaving at 7:00 am.Since the airportis a bit farfromwhere I liveIneed toset fftwoby step.hour. We can get there in a quarter.I don’t need to worry about forgetting thingshours before the take-off time. I'm afraid it'll beM:I hope so.or rushing.5.M:Hello! Is that Linda speaking?too early in the morning for me to take a taxi. So表达感受：WSorry,shesnt nhis isher motherhI need you to take me to the airport. Please waitAfter finishing everything,I feel relaxed andfor me at 5:00 tomorrow morning.has gone to the hospital.proud.M:ThehospitalWhat’s up?Is there anythingI've checked the weather report. Though it's feel more relaxed and enjoy more free time.fine today, it'll turn bad tomorrow morning.Sowrong with her?It really makes my life more organized.W:Noshehasjust gone to seeher friend whodon't forget to take an umbrella.【范文展示】broke her legs.Here I thank you again for all that you haveDear Emily,第二节：I'm glad to hear from you. You asked me how I听下面3段对话或独白。每段对话或独白enjoy teaching here and will never forget themanage my time. Now let me share one of my后有几个小题，从题中所给的A、B、C三个选ways with you.come back some day. I left some books to your项中选出最佳选项，并标在试卷的相应位置。Imake a to-do list every morning and follow itlibrary. hope they will beuseful toyour students.听每段对话或独白前，你有时间阅读各小题，during thdayItcludemymworkradngThat' s all. See you tomorrow.每小题5秒钟。听完后，各小题将给出5秒钟time and housework. I follow the list and finish的作答时间。每段对话或独白读两遍。参考答案the tasks one by one. It helps me plan my day听下面一段对话，回答第6至第7两个小题。（Onepossible version客观题除外）clearly and avoid wasting time.M: Hi Cathy! You look hapy.第一部分：After finishing everything,I feel relaxed andW:HiBen.Iwent to the Science and Technology1-5BCBBC6-10 CCBAC 11-15 BAACB第二部分：because Idontleave things until the lastminuMuseum with my uncle and aunt yesterday.16-18AAC19-22DBBC 23-26ABDDIhope my idea can help you.Looking forward toM: What did you do there?27-30BBDA 31-34DBCAyour reply!35.I agree with Clara's because choosing seatsinstruments. I also learned more about YangYours,teaches us to be responsible and lets us feelLi HuaLiwei and Wang Yaping.relaxed in class. / I agree with Jacob's becauseM:Yang Liwei and Wang Yaping are great as-第T2期teachers can arrange seats better to avoidtronauts in China.B1版Keys:A 1-5ABBCA B 1-5BDBCAdistractions and help students focus.B2B3B4版Keys:W:Yes, they are so great and we are all proud of第三部分：中考英语全真模拟训练（二）them.第一节听力原文及参考答案M:Iamntrested in science,tooWould you love36-40 ACABD41-45BACDA听力原文to go to the Science and Technology Museum46-50 CABCD第一节：again with me next Saturday?第二节听下面5段对话。每段对话后有一个小W: Sure, I’d love to.And I will ask my sister51.at first52.Instead53.rubbish题，从题中所给的A、B、C三个选项中选出最Laura to go with us. We will go there by56.Japan54.writes55.requests佳选项，并标在试卷的相应位置。听完每段对bike. How about you?59.dictionary57.square58.short话后，你都有10秒钟的时间来回答有关小题M:I live a little far. I will take the underground60.fits/suits61.rules62.real/true和阅读下一小题。每段对话仅读一遍。there.63.visiting64.area65.joy/happiness1.M:Alice,where is my bag?I can't find it on听下面一段对话，回答第8至第10三个第三节the table.小题。66. silence67.replied68.BeforeW:You always put your things everywhere. IsM: Daisy, Christmas is coming. Are you going69.her70.twice71.carefullyit on the sofa?back to New York to celebrate it with your72.The73.were walkingfamily?（下转B2版）发行总代理：北京九州新时代书报刊发行有限公司 订报热线：400-013-0021广告经营许可证号：340000000079《双语学报）七、八、九年级每期4开8版，彩色印刷，每学期总定价78.00元。